用遗传编程优化代数多重网格循环，提升求解效率。
Evolving Algebraic Multigrid Methods Using Grammar-Guided Genetic Programming
- 用语法引导的遗传编程生成任意形状的多重网格循环
- 在3D各向异性问题上性能优于传统V/F/W循环
- 适合需要高效线性方程组求解的科学计算场景
尽管多重网格方法被证明是渐近最优的，但其效率高度依赖于组件的精心选择，且通常局限于V、F、W等标准循环类型。本文利用语法规则生成任意形状的循环，使每一步的平滑器及其松弛权重可独立选择，形成灵活的多重网格循环。该方法结合语法规则与遗传编程，在hypre库中实现灵活代数多重网格（AMG）方法，并分别针对两类场景进行优化：独立的3D各向异性问题求解器，以及用于多物理场代码的共轭梯度预处理器。实验表明，经优化的灵活循环在效率和性能上均优于标准循环类型。
原文摘要 · Abstract (English)
Multigrid methods despite being known to be asymptotically optimal algorithms, depend on the careful selection of their individual components for efficiency. Also, they are mostly restricted to standard cycle types like V-, F-, and W-cycles. We use grammar rules to generate arbitrary-shaped cycles, wherein the smoothers and their relaxation weights are chosen independently at each step within the cycle. We call this a flexible multigrid cycle. These flexible cycles are used in Algebraic Multigrid (AMG) methods with the help of grammar rules and optimized using genetic programming. The flexible AMG methods are implemented in the software library of hypre, and the programs are optimized separately for two cases: a standalone AMG solver for a 3D anisotropic problem and an AMG preconditioner with conjugate gradient for a multiphysics code. We observe that the optimized flexible cycles provide higher efficiency and better performance than the standard cycle types.
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